New extended superconformal sigma models and Quaternion Kahler manifolds

Abstract

Quaternion Kahler manifolds are known to be the target spaces for matter hypermultiplets coupled to N=2 supergravity. It is also known that there is a one-to-one correspondence between 4n-dimensional quaternion Kahler manifolds and those 4(n+1)-dimensional hyperkahler spaces which are the target spaces for rigid superconformal hypermultiplets (such spaces are called hyperkahler cones). In this paper we present a projective-superspace construction to generate a hyperkahler cone M^{4(n+1)}_H of dimension 4(n+1) from a 2n-dimensional real analytic Kahler-Hodge manifold M^{2n}_K. The latter emerges as a maximal Kahler submanifold of the 4n-dimensional quaternion Kahler space M^{4n}_Q such that its Swann bundle coincides with M^{4(n+1)}_H. Our approach should be useful for the explicit construction of new quaternion Kahler metrics. The results obtained are also of interest, e.g., in the context of supergravity reduction N=2 --> N=1, or alternatively from the point of view of embedding N=1 matter-coupled supergravity into an N=2 theory.

arXiv comment30 pages

References in corpus (32)

• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• String loop corrected hypermultiplet moduli spaces
• String loop corrections to the universal hypermultiplet
• Superconformal Hypermultiplets
• 4D N = 2 Supergravity and Projective Superspace
• Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry
• Superconformal Symmetry and Correlation Functions
• Projective Superspace as a Double--Punctured Harmonic Superspace
• On conformal supergravity and projective superspace
• Hypermultiplets and Topological Strings
• Feynman Rules in N=2 Projective Superspace I: Massless hypermultiplets
• Superspace Effective Actions for 4D Compactifications of Heterotic and Type II Superstrings
• Twistors and Black Holes
• On compactified harmonic/projective superspace, 5D superconformal theories, and all that
• Super-Weyl invariance in 5D supergravity
• Anomalous Magnetic Properties of Sr2YRuO6
• Different representations for the action principle in 4D N = 2 supergravity
• Properties of hyperkahler manifolds and their twistor spaces
• Feynman rules in N=2 projective Superspace II: Massive hypermultiplets
• Supersymmetry reduction of N-extended supergravities in four dimensions
• Consistent reduction of N=2 -> N=1 four dimensional supergravity coupled to matter
• On superconformal projective hypermultiplets
• Quantum Corrections to the Universal Hypermultiplet and Superspace
• The CNM-Hypermultiplet Nexus
• Field theory in 4D N=2 conformally flat superspace
• 4D, N = 2 Supersymmetric Off-shell Sigma-Models on the Cotangent Bundles of Kahler Manifolds
• On N = 2 supergravity and projective superspace: Dual formulations
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Hyperkahler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace
• Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics
• Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces
• A note on conformal symmetry in projective superspace

Cited by in corpus (9)

• Off-shell supergravity-matter couplings in three dimensions
• Conformal supergravity in five dimensions: New approach and applications
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Lectures on nonlinear sigma-models in projective superspace
• Effective action of three-dimensional extended supersymmetric matter on gauge superfield background
• Extended supersymmetric sigma models in AdS_4 from projective superspace
• N = 2 supersymmetric sigma-models and duality
• Thermalization and prethermalization in the soft-wall AdS/QCD model
• New supersymmetric sigma-model duality